Suggested languages for you:

Americas

Europe

Q. 22

Expert-verifiedFound in: Page 156

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Graph the function $f$ by starting with the graph of $y={x}^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

$f\left(x\right)=(x-3{)}^{2}-10$

The required graph is shown below:

The given function is:

$f\left(x\right)=(x-3{)}^{2}-10$

In the function $f\left(x\right)=a(x-h{)}^{2}+k,a$ is a constant and $(h,k)$ is the vertex.

In the given function $a=1,h=3,k=-10$. It means the graph of the given function is a parabola that opens up and has its vertex at $(3,-10)$ and its axis of symmetry is the line $x=3$.

The graph of $y={x}^{2}$ shifts 3 units right and 10 units down.

First plot the graph of $y={x}^{2}$ then shift it 3 units right and then shift the resulted graph 10 units down to get the graph of the function $f\left(x\right)=(x-3{)}^{2}-10$.

The required graph is shown below:

Using a graphing utility, we get a graph that is the same as the above graph.

94% of StudySmarter users get better grades.

Sign up for free